algebraic geometry

Automorphism groups of non-normal affine toric surfaces

arXiv:2606.14234

summary

The paper studies automorphism groups of non‑normal affine toric surfaces and shows that, unlike the normal case, the connected component need not be generated by the acting torus and root subgroups, providing an explicit counterexample.

Abstract

We investigate the automorphism group of a non-normal affine toric surface. It is known that for a normal affine toric surface the connected component of the automorphism group is generated by the acting torus and root subgroups. While this fact is also true for some classes of non-normal affine toric surfaces, it fails in general. We give an example of a non-normal affine toric surface, whose singular locus is a point and the connected component of the automorphism group is not generated by the acting torus and root subgroups.

16 pages, 4 figures

Topics & keywords

#toric surfaces#automorphism groups#non-normal varieties#affine geometry#algebraic groupsautomorphism grouptoric surfacenon-normalconnected componentroot subgroupstorus
Automorphism groups of non-normal affine toric surfaces · wovepaper